Mathematics – Dynamical Systems
Scientific paper
2012-01-04
Mathematics
Dynamical Systems
Six pages and three figures. To be presented at the mini symposium "Classical and Quantum Circuits", MathMod Conference in Vie
Scientific paper
Meminductors and memcapacitors do not allow a Lagrangian formulation in the classical sense since these elements are nonconservative in nature and the associated energies are not state functions. To circumvent this problem, a different configuration space is considered that, instead of the usual loop charges, consist of time-integrated loop charges. As a result, the corresponding Euler-Lagrange equations provide a set of integrated Kirchhoff voltage laws in terms of the element fluxes. Memristive losses can be included via a second scalar function that has the dimension of action. A dual variational principle follows by considering variations of the integrated node fluxes and yields a set of integrated Kirchhoff current laws in terms of the element charges. Although time-integrated charge is a somewhat unusual quantity in circuit theory, it may be considered as the electrical analogue of a mechanical quantity called absement. Based on this analogy, simple mechanical devices are presented that can serve as didactic examples to explain memristive, meminductive, and memcapacitive behavior.
No associations
LandOfFree
Memory Elements: A Paradigm Shift in Lagrangian Modeling of Electrical Circuits does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Memory Elements: A Paradigm Shift in Lagrangian Modeling of Electrical Circuits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Memory Elements: A Paradigm Shift in Lagrangian Modeling of Electrical Circuits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-608787